# Incorrect Result Raising 10 to Very Large/Very Small Power

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##### SYMPTOMS
In the versions of Microsoft Excel listed at the beginning of this article,if you enter a formula in which the value 10 is raised to either a verylarge power or a very small power, the formula may return an incorrectresult:
`   10 Raised to       Expected Result   Actual Result   -------------------------------------------------------------------   very large power   #NUM! error       0, 0.1   very small power   0                 #DIV/0! error, 10^<some value>`
NOTE: These problems do not occur in earlier versions of Microsoft Excel.Also, the problems do not occur when you raise a value other than 10 toa very large power or a very small power; for example, =9^10000000000correctly returns a #NUM! error.
##### CAUSE
These problems occur when you enter a formula in which the value 10 israised to a power in one of the following ranges:

• greater than or equal to 2^31 (2,147,483,648) and less than or equal to 10^308 (1 followed by 308 zeroes) -or-

• less than or equal to -(2^31) (-2,147,483,648) and greater than or equal to -(10^308) (-1 followed by 308 zeroes)
For example:
`   Formula you type          Value returned   ----------------------------------------   =10^2147483648            0   =10^10000000000           0.1   =10^(10^308)              0.1				`
These formulas should all return a #NUM! error, because the largestpositive number allowed in Microsoft Excel is 9.99999999999999E+307,which is just less than 10^308.Or:
`   Formula you type          Value returned   ----------------------------------------   =10^-2147483648           #DIV/0!   =10^-4294966989           1E+307   =10^-4294967295           10   =10^-(10^308)             10				`
These formulas should all return the value 0, because the smallestpositive number allowed in Microsoft Excel is 1E-307,which is just above 0.
##### WORKAROUND
To prevent this problem from occurring, make sure that formulas in yourworkbooks do not raise the number 1.797 to a power larger than 308 or the number 2.225 smaller than -308.
##### STATUS
Microsoft has confirmed this to be a problem in the Microsoft productslisted at the beginning of this article.
Microsoft Excel supports positive values almost as large as 10^308 (aone followed by 308 zeroes) and almost as small as 10^-308 (a decimalpoint, followed by 308 zeroes and a one). Similar negative values arealso supported. Smaller values are rounded to 0, and larger values areconverted into a #NUM! error value.

For comparison, note that the estimated number of elementary particles inthe known universe is 10^80, or a one followed by 80 zeroes. The smallestvalue used in physics is roughly 10^-33 centimeters, the scale at whichquantum fluctuations are believed to exist. These values are well withinthe limits supported by Microsoft Excel; so, Microsoft Excel can workwith any meaningful number in the universe.

With respect to the largest formula shown above: note that a googol is10^100, or a 1 followed by 100 zeroes, and that a googolplex is 10^googol,or a 1 followed by 10^100 zeroes.

The correct result of the third formula shown above, =10^(1E+308), isa 1 followed by 10^308 zeroes. So, the result of the third formula isequivalent to the following:
googolplex*googolplex*googolplex*(10^(10^8))
So, it would take over (1 followed by 10^307 zeroes) universes tocontain (1 followed by 10^308 zeroes) elementary particles.
XL97 googol googolplex mantissa exponent XL
Properties

Article ID: 172911 - Last Review: 10/07/2013 05:16:24 - Revision: 1.1

Microsoft Excel 97 Standard Edition, Microsoft Excel 98 for Macintosh

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